I often see a lot of software saying they can connect to the Losmandy G11 or a LX200 compatible mount (which the G11 is), but I'm always confused about how is the G11 physically connected to the computer?

My laptop only has USB and the G11's Gemini has RS232 I believe.

Is there a way to connect to this or do I need a RS232 capable computer?

You need to get a USB to RS232 adapter. They're quite easy to find online and you might be able to find one at your local Best Buy. Just make sure you get one that has drivers compatible with your operating system. I've seen some that have trouble with Vista and 64-bit Windows.

Just buy a good one and it will work fine. You just plug it into the G-11 serial port and make sure the control software is set to the port of the USB to Serial adapter. Then you can control it with Starry Night or The Sky or other software. Plus you can use this cable to program the G-11 or use PemPro to set the PEC to reduce PE. Be sure you use the proper cable though, if in doubt, check it out before plugging it in, there are some with reversed wires.
Blueman

Saad, a good RS232 converter will cost a bit. I recommend you stay away from the cheapest ones. I also recommend you get a 2- or 4-port unit because eventually you'll need it for a focuser, filter wheel, or some other item that connects via RS232. I use this one and it's been very reliable.

Can't help with your connection requirements but I can confirm that the Keyspan is very good.

I bought a cheaper (although supposedly good quality) adapter to update my Argo Navis and it just wouldn't work.

After getting in touch with Argo Navis (great service btw) they recommended the Keyspan and it worked faultlessly....I don't have the Gemini on my G11 just the Argo Navis so can't advise on your connection needs.